A Numerical Approach to the Problem of Multiple Scattering of Electromagnetic Radiation

An iterative method is presented for evaluating the multiple scattering of electromagnetic radiation applicable to a discrete distribution of scatterers. The approach saves computational time by using a two-point function representing the nth-order scattering to evaluate the (n+ 1)th-order field. In order to achieve this, the intermediate results of each iteration are stored and retrieved as required.     

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Exact mathematical expressions for the intrinsic electromagnetic (EM) cross–sections (i.e. extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous non–absorptive medium are derived. The multipole expansion method in cylindrical coordinates and the translational addition theorem, applicable to any range of frequencies or particle sizes are used. An effective EM field, incident on the probed cylinder is defined first, which includes the initial and re-scattered field from the second cylinder. It is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross–sections. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies per unit-length for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross–sections.     

An hp‐adaptive finite element method for scattering problems in computational electromagnetics

An hp‐adaptive finite element (FE) approach is presented for a reliable, efficient and accurate solution of 3D electromagnetic scattering problems. The radiation condition in the far field is satisfied automatically by approximation with infinite elements (IE). Near optimal discretizations that can effectively resolve local rapid variations in the scattered field are sought adaptively by mesh refinements blended with graded polynomial enrichments. The p‐enrichments need not be spatially isotropic. The discretization error can be controlled by a self‐adaptive process, which is driven by implicit or explicit a posteriori error estimates. The error may be estimated in the energy norm or in a quantity of interest. A radar cross section (RCS) related linear functional is used in the latter case. Adaptively constructed solutions are compared to pure uniform p approximations. Numerical, highly accurate, and fairly converged solutions for a number of generic problems are given and compared to previously published results. Copyright © 2004 John Wiley & Sons, Ltd.     

Scattering of the electromagnetic waves from a rough surface

The electromagnetic field scattered by a rough surface of a semi-infinite body is computed up to the second order of a perturbation scheme with the surface roughness as a perturbation parameter. The calculations are based on the equation of motion of the polarization within the Lorentz–Drude (plasma) model of polarizable, non-magnetic, homogeneous matter. The surface roughness contributes both to the main (specularly) reflected and refracted fields and diffuse scattering, or gives rise to secondary (second-order) diffraction peaks for a regular grating. The calculations are performed both for the s- and p-waves. Two-dimensional modes, resonant at certain frequencies, are identified, confined to and propagating only on the surface, as a consequence of the surface roughness.     

Generalized debye series for acoustic scattering from objects of separable geometric shape

Summary In a classical paper of 1908, Debye has resolved the electromagnetic field scattered by a dielectric cylinder into a series of waves multiply internally reflected in the cylinder. For acoustic scattering by elastic cylinders, a corresponding series was derived from the conventional solution (obtained by satisfying the overall or global continuity conditions) by Brill and Überall, taking into account mode conversions of longitudinal (L) into transverse (T, shear) waves, or vice versa, upon internal scattering in a some-what involved fashion. In a series of papers, Gérard has shown that this approach could be greatly simplified by introducing local reflection and transmission coefficients at each interface, which is suitable for generalizing the Debye series to the case of elastic waves coupled by the continuity conditions at the external and each of any possible (multiple) internal interfaces of the scattering object. The approach is then applicable to all elastic objects for which surface and interfaces form coordinate surfaces of any separable geometry; the corresponding derivation is given here in the most general fashion, and is concretely illustrated by the examples of an elastic plate, infinite cylinder and sphere.     

<Emphasis Type="Italic">SH</Emphasis>-wave intromission concept

The existence of an SH-wave incidence angle for which the reflected amplitude is zero (SH-wave intromission angle) is established for the case of plane-wave scattering by a planar interface joining two homogeneous, isotropic, and linearly elastic half-spaces. Such an incidence angle is numerically shown to exist for two combinations of bimaterial interface properties. The SH-wave intromission angle is roughly parallel to the electromagnetic Brewster angle and the acoustic P-wave intromission angle, and the concept should find new applications for non-intrusive characterization of interfaces.     

Scattering simulations in inhomogenous volumes for scanning near-field optical microscopy

Abstract

This paper describes finite-element techniques to simulate scattering of electromagnetic radiation from objects in inhomogeneous solution spaces. The motivation for the work is the development of software to model field interactions at surfaces for scanning near-field optical microscopes. The calculation is performed in a computational anechoic chamber—a finite volume surrounded by an absorbing layer to simulate free space. The volume may consist of any configuration of materials, including lossy dielectrics and ferrites. The first step in the procedure is to find a distribution of element current sources consistent with the absorbing boundaries that generate the desired unperturbed wave solution. The base solution is not limited to simple plane waves. It may consist of any valid electromagnetic disturbance including mixed propagating and evanescent waves. The second step is to introduce one or more scattering objects and to solve finite-element equations for the perturbed fields. One advantage of the approach is that the boundaries need only absorb the scattered field components. Another useful feature for the microscopy calculations is that the method is equally effective for near and far fields. In simulations of small object scattering the absorbing boundary can be at a distance much less than a wavelength.     

Scattering of Light from Two Interacting Spherical Particles

Abstract

Linear optical properties of two spherical particles interacting via their dipole fields are studied. The dipole susceptibility and cross-sections of extinction, scattering and dissipation are found as functions of susceptibility χ₀ of an isolated particle. The case of arbitrary distance between particles is considered (which include interaction in near-zone, transitional-zone and far-zone). It is shown, that radiative energy losses of an oscillating dipole give rise to a finite phase shift between oscillations of the dipole and it's electromagnetic field in the near-zone. Application of this fact to the problem of two interacting dipoles leads to appearance of two additional resonances of susceptibility of the pair with radiative half-width tending to be zero when r₁₂→0 as (r₁₂/λ)², where r ₁₂ is the distance between particles.     

Experimental investigation of microsegregation in low frequency electromagnetic casting 7075 aluminum alloy

7075 aluminum alloy ingots were prepared by the process of low frequency electromagnetic casting (low frequency electromagnetic casting = LFEC) and conventional direct chill (direct chill = DC) casting, respectively. The effects of low frequency electromagnetic field on microsegregation were investigated from eutectic analysis and electro probe microanalysis (EPMA). It was found that the amount of the eutectic, which was composed of α‐Al (aluminum phase), T phase and MgZn₂ was decreased markedly. In contrast, the solute concentration profiles which depend on solid fraction were increased to a certain extent with the presence of low frequency electromagnetic field. The effective distribution coefficient k_e was calculated, and the values of k_e for solutes in the LFEC sample were bigger than those in the DC sample. The LFEC process alleviated the microsegregation in 7075 aluminum alloy.     

Propagation of the electric correlation matrix and the van Cittert–Zernike theorem for random electromagnetic fields

The basic mathematical tool of the theory of random, statistically stationary electromagnetic optical fields is a 3?×?3 correlation matrix of its electric field. In this paper we derive formulae for propagation of this matrix from a plane z?=?0 into the half-space z?>?0, and we find an analogue for electromagnetic fields to the propagation law derived by Zernike for scalar fields.     

On the theory of elastic scattering of electromagnetic waves by atoms

A Hamiltonian describing the elastic interaction of electromagnetic radiation (EMR) with an atom is obtained using the invariant theory of perturbations in the limit of EMR wavelengths λ significantly exceeding the atom size a₀. An exact expression for the interaction amplitude is obtained, and the probability of EMR scattering on the atom is calculated. It is established that the scattering probability at large λ is proportional to the squared frequency of monochromatic EMR. It is shown that, in the limit of large wavelengths, the formula h∼(ω/c)⁴ v ₀ for the extinction coefficient is inapplicable and the relation h=Aω² becomes valid, where A is a definite coefficient.     

Coherent pairing of excitons in insulators and semiconductors

A microscopic theory is developed concerning the coherent pairing of Wannier-Mott type excitons in insulators and semiconductors. The coherent pairing of excitons occurs in the presence of a resonant electromagnetic field and the resulting energy gap is in competition with that induced by the electromagnetic field. Due to the electrical neutrality of the electron-hole pairs, the excitation spectrum is of the excitonic insulator type and the presence of the electromagnetic field results in the splitting of the energies of excitation. The expression for the coherent gap function depends on the exciton density, the effective exciton mass, the exciton-exciton interaction, and the effective energy band gap, which is equal to the difference between the transition frequency and the frequency of the field and the binding energy of the exciton. Under resonance conditions and at temperatures below some valueT _c , the biexciton state can exist provided that the dielectric gap is less than that for the biexciton state. The ground-state energy resulting from the coherent pairing of excitons is calculated and is found to be lower in energy than the normal exciton state. This indicates the existence of a bound biexciton state as long as there is a net attractive exciton-exciton interaction.Issued as NRCC No. 15395.     

A compact stripline transducer for measuring a pulsed electromagnetic field

A stripline transducer for measuring a pulsed electromagnetic field is proposed, the shape of which enables its electrical length to be increased considerably while keeping its actual dimensions small. An expression is obtained for the potential-difference distribution along the stripline transducer when it is excited by a pulsed electromagnetic field of step-shaped form. The theoretical results obtained are confirmed by experiment.Translated from Izmeritel'naya Tekhnika, No. 4, pp. 45–46, April, 1994.     

Stability convergence and accuracy of the DuFort and Frankel difference diagram approximating a class of non-linear parabolic field equations

The paper presents a method of calculation for the transient electromagnetic field in a steel rotor screen of a superconducting generator. Using the difference method, the spatial–temporal distributions of the electromagnetic field have been calculated as a result of solving the non-linear partial differential equation for the vector potential A (in space Ω(r, θ,t)). For the difference diagram the conditions of stability and convergence have been determined.     

Ultrahigh Responsivity UV Photodetector Based on Cu Nanostructure/ZnO QD Hybrid Architectures

Strong near‐surface electromagnetic field formed by collective oscillation of electrons on Cu nanostructure a shows a strong dependence on geometry, offering a promising approach to boost the light absorption of ZnO photoactive layers with enhanced plasmon scattering. Here, a facile way to fabricate UV photodetectors with tunable configuration of the self‐assembled Cu nanostructures on ZnO thin films is reported. The incident lights are effectively confined in ZnO photoactive layers with the existence of the uplayer Cu nanostructures, and the interdiffusion of Cu atoms during fabrication of the Cu nanostructures can improve the carrier transfer in ZnO thin films. The optical properties of the hybrid architectures are successfully tailored over a control of the geometric evolution of the Cu nanostructures, resulting in significantly enhanced photocurrent and responsivity of 2.26 mA and 234 A W^?1 under a UV light illumination of 0.62 mW cm^?2 at 10 V, respectively. The photodetectors also exhibit excellent reproducibility, stability, and UV–visible rejection ratio (R_{370 nm}/R_{500 nm}) of ≈370, offering an approach of high‐performance UV photodetectors for practical applications.     

Investigation of the electric field excited by a personal computer

The electromagnetic field produced by a personal computer at frequencies in the 20 Hz-30 MHz range is investigated experimentally. Data are obtained on the spectral composition and polarization of the electric component of the electromagnetic field. Measurements of the spatial structure and the field strength in the front half-space of the plane of the monitor are presented.Translated from Izmeritel'naya Tekhnika, No. 7, pp. 59–61, 1994.     

Scattering analysis of conducting axisymmetic particles using the extended boundary condition method with discrete source

Abstract

In this paper the extended boundary condition method with discrete sources (DS) is introduced for the electromagnetic scattering problem of a conducting axisymmetric particle. The approximate solution is constructed as a linear combination of “Mie-potentials” with different origins. In order to take advantage of the rotational symmetry the DS are distributed on an auxiliary curve in the plane of the generatrix. The complete system of vector functions have an explicit exp (jm?-dependence which lead to a decoupling of the scattering problem over each azimuthal mode. It is shown that with the method discussed herein, the computational efficiency can be improved in comparison to that which use DS distributed on auxiliary surfaces.     

Wavelet-accelerated regularization methods for hyperthermia treatment planning

Cancer therapy by hyperthermia treatment aims to heat up the region of the tumor while keeping the surrounding body below a prespecified temperature. The heating is achieved by an electromagnetic field generated by several antennae which are placed around the patient. The hyperthermia problem is to determine the parameters of the antennae, s.t. the resulting electromagnetic field is optimal with respect to some prescribed quality criterion. Iterative optimization algorithms require the solution of large, dense linear systems in each iteration step. We investigated modifications of standard regularization methods for inverse problems where the system matrix A is replaced by a family of sparse approximations {A_k}. An adaptation strategy for choosing the approximation level, which leads to the same convergence rates as iteration schemes with the full matrix A, is proved. Wavelet compression techniques originally designed for applications in image processing are used to compute the approximating family {A_k} leading to accelerated iteration schemes. They are finally applied to optimize hyperthermia treatment planning. © 1996 John Wiley & Sons, Inc.     

Experimental proof of the existence of a surface electromagnetic wave

Results of experiments for the observation of surface electromagnetic waves (SEWs) in the decameter range (10 and 15 MHz) excited by a vertical dipole and propagating above the ice-coated surface of a salt lake over a distance of up to 1.2 km are considered. It is shown that the SEW decays much more weakly than the “ground” ray. An analysis of the field of radiation from the vertical dipole reveals the presence of a wave with an amplitude decaying with the distance R approximately as 1/R ^1/2, which corresponds to the SEW divergence. The absolute values of the radiation attenuation function |W| are significantly greater than unity and reach |W| ≈ 2, which also corresponds to the SEW. Experimental data on the SEW damping agree with the results of numerical calculations of the electromagnetic field in the system under consideration.     

A Polarized Transfer Matrix for Electromagnetic Waves in Structured Media

Abstract

The study of electromagnetic systems with dielectric or magnetic properties that vary spatially on or below the scale set by the wavelength of the radiation considered is of interest both in the field of photonic band gap materials and in that of random multiple scattering media. A key calculation technique in both areas is the transfer matrix. We derive a new transfer matrix, written in the language of scattering between transverse polarized wave states. This could be used in either photonic band calculations or in disordered media calculations. We demonstrate the use of the new transfer matrix to describe transport through a layered random dielectric in the Rayleigh scattering regime. This problem has considerable similarities to that of non-interacting electrons in a one-dimensional random potential. A complete solution for one polarization can be given by the use of group theoretical results. The other polarization exhibits pronounced dipole effects which can easily be calculated to lowest order.